{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4a02d642-5482-447b-a830-1bb571b0c1c8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0]\n",
      "\n",
      "The minimum energy appears 4 times.\n",
      "\n",
      "Configurations corresponding to the minimum energy values:\n",
      "\n",
      "\n",
      "[0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0]\n",
      "[1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0]\n",
      "[1.0, 2.0, 1.0, 2.0, 2.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0, 2.0, 1.0, 2.0, 1.0]\n",
      "[2.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0, 2.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0]\n"
     ]
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "using Random\n",
    "using Plots\n",
    "using Statistics \n",
    "using DataFrames\n",
    "using DelimitedFiles\n",
    "\n",
    "function generate(n)\n",
    "    return zeros(Int, n*n)\n",
    "end\n",
    "\n",
    "#ising = zeros(Int, N)\n",
    "\n",
    "# Function to compute first, second, and third nearest neighbors\n",
    "function neighbor_honeycomb(n)\n",
    "    nbor1 = zeros(Int, 3, n * n)\n",
    "    nbor2 = zeros(Int, 6, n * n)\n",
    "    nbor3 = zeros(Int, 3, n * n)\n",
    "\n",
    "    for ispin in 1:(n * n)\n",
    "       \n",
    "        iy = div(ispin - 1, n)\n",
    "        ix = ispin - 1 - iy * n\n",
    "\n",
    "        # Calculate indices for neighboring spins with periodic boundary conditions\n",
    "        ixp = mod(ix + 1, n)       \n",
    "        iyp = mod(iy + 1, n)      \n",
    "        ixm = mod(ix - 1 + n, n)   \n",
    "        iym = mod(iy - 1 + n, n)   \n",
    "        \n",
    "        # Calculate second nearest indices for neighboring spins\n",
    "        ixpp = mod(ix + 2, n)     \n",
    "        ixmm = mod(ix - 2 + n, n)  \n",
    "        iypp = mod(iy + 2, n)      \n",
    "        iymm = mod(iy - 2 + n, n) \n",
    "\n",
    "        # First nearest neighbors\n",
    "        nbor1[1, ispin] = iy * n + ixp + 1 \n",
    "        nbor1[3, ispin] = iy * n + ixm + 1  \n",
    "\n",
    "        if iy % 2 == 1\n",
    "            if ix % 2 == 1\n",
    "                nbor1[2, ispin] = iyp * n + ix + 1  \n",
    "\n",
    "                # Second nearest neighbors\n",
    "                nbor2[1, ispin] = iy  * n + ixpp + 1       \n",
    "                nbor2[2, ispin] = iyp * n + ixp  + 1      \n",
    "                nbor2[3, ispin] = iyp * n + ixm  + 1       \n",
    "                nbor2[4, ispin] = iy  * n + ixmm + 1      \n",
    "                nbor2[5, ispin] = iym * n + ixm  + 1        \n",
    "                nbor2[6, ispin] = iym * n + ixp  + 1        \n",
    "\n",
    "                # Third nearest neighbors\n",
    "                nbor3[1, ispin] = mod(iyp * n + ixpp, n*n) + 1  \n",
    "                nbor3[2, ispin] = mod(iyp * n + ixmm, n*n) + 1\n",
    "                nbor3[3, ispin] = mod(iym * n + ix,   n*n) + 1    \n",
    "                \n",
    "            else\n",
    "                nbor1[2, ispin] = iym * n + ix + 1 \n",
    "\n",
    "                # Second nearest neighbors\n",
    "                nbor2[1, ispin] = iy  * n + ixpp + 1     \n",
    "                nbor2[2, ispin] = iyp * n + ixp  + 1    \n",
    "                nbor2[3, ispin] = iyp * n + ixm  + 1    \n",
    "                nbor2[4, ispin] = iy  * n + ixmm + 1    \n",
    "                nbor2[5, ispin] = iym * n + ixm  + 1    \n",
    "                nbor2[6, ispin] = iym * n + ixp  + 1   \n",
    "\n",
    "                # Third nearest neighbors\n",
    "                nbor3[1, ispin] = mod(iyp * n + ix, n*n) + 1 \n",
    "                nbor3[2, ispin] = mod(iym * n + ixmm, n*n) + 1 \n",
    "                nbor3[3, ispin] = mod(iym * n + ixpp, n*n) + 1\n",
    "                \n",
    "            end\n",
    "        else\n",
    "            if ix % 2 == 1\n",
    "                nbor1[2, ispin] = iym * n + ix + 1 \n",
    "\n",
    "                # Second nearest neighbors\n",
    "                nbor2[1, ispin] = iy  * n + ixpp + 1   \n",
    "                nbor2[2, ispin] = iyp * n + ixp  + 1    \n",
    "                nbor2[3, ispin] = iyp * n + ixm  + 1    \n",
    "                nbor2[4, ispin] = iy  * n + ixmm + 1       \n",
    "                nbor2[5, ispin] = iym * n + ixm  + 1       \n",
    "                nbor2[6, ispin] = iym * n + ixp  + 1       \n",
    "\n",
    "                # Third nearest neighbors\n",
    "                nbor3[1, ispin] = mod(iyp * n + ix, n*n) + 1   \n",
    "                nbor3[2, ispin] = mod(iym * n + ixmm, n*n) + 1 \n",
    "                nbor3[3, ispin] = mod(iym * n + ixpp, n*n) + 1 \n",
    "\n",
    "            else\n",
    "                nbor1[2, ispin] = iyp * n + ix + 1 \n",
    "\n",
    "                # Second nearest neighbors\n",
    "                nbor2[1, ispin] = iy  * n + ixpp + 1      \n",
    "                nbor2[2, ispin] = iyp * n + ixp  + 1     \n",
    "                nbor2[3, ispin] = iyp * n + ixm  + 1    \n",
    "                nbor2[4, ispin] = iy  * n + ixmm + 1       \n",
    "                nbor2[5, ispin] = iym * n + ixm  + 1      \n",
    "                nbor2[6, ispin] = iym * n + ixp  + 1       \n",
    "\n",
    "                # Third nearest neighbors\n",
    "                nbor3[1, ispin] = mod(iyp * n + ixpp, n*n) + 1 \n",
    "                nbor3[2, ispin] = mod(iyp * n + ixmm, n*n) + 1 \n",
    "                nbor3[3, ispin] = mod(iym * n + ix, n*n) + 1   \n",
    "                \n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    return nbor1, nbor2, nbor3\n",
    "end\n",
    "\n",
    "function calculate(ising, nbor1, nbor2, nbor3, J1, J2, J3, N, U, μ)\n",
    "    e = 0.0\n",
    "    neighbor_sum = 0.0\n",
    "    for i in 1:N \n",
    "        for j in 1:3\n",
    "          if ising[i] != ising[nbor1[j,i]]\n",
    "                    neighbor_sum = neighbor_sum - J1\n",
    "          end\n",
    "        end    \n",
    "        for j in 1:6\n",
    "           if ising[i] != ising[nbor2[j, i]]\n",
    "           neighbor_sum = neighbor_sum - J2\n",
    "           end          \n",
    "        end\n",
    "        for j in 1:3\n",
    "           if ising[i] != ising[nbor3[j, i]]\n",
    "           neighbor_sum = neighbor_sum - J3                    \n",
    "           end\n",
    "        end\n",
    "    end\n",
    "    e = e + neighbor_sum\n",
    "    for i in 1:N\n",
    "        e = e + (U / 2) * ising[i] * (ising[i] - 1)\n",
    "    end\n",
    "#   我把两项分开算了 也可以合起来\n",
    "    for i in 1:N\n",
    "        e = e - μ * ising[i]\n",
    "    end\n",
    "    e = e / 2\n",
    "#    e = e / N\n",
    "    m = (sum(ising)) \n",
    "    return e, m\n",
    "end\n",
    "\n",
    "n = 4\n",
    "N = n * n \n",
    "J1 = 1\n",
    "J2 = -2\n",
    "J3 = 0\n",
    "U = 1\n",
    "μ = 0.5\n",
    "# 记得改参数\n",
    "# J4 = 0\n",
    "# J2_values = -2:0.5:0     \n",
    "# J3_values = 0:0.5:2    \n",
    "\n",
    "#save_dir = \"C:/Ising_3_try\"\n",
    "#ispath(save_dir) || mkpath(save_dir)\n",
    "\n",
    "results = []\n",
    "final_results = [] \n",
    "\n",
    "e_steps = zeros(3^N)\n",
    "m_steps = zeros(3^N)\n",
    "ising_steps=zeros(3^N, N)\n",
    "ising = generate(n)\n",
    "nbor1, nbor2, nbor3 = neighbor_honeycomb(n)\n",
    "\n",
    "for k1 in 0:3^N - 1\n",
    "    num1 = lpad(string(k1, base=3), N, '0')\n",
    "    for j in 1:N\n",
    "        ising[j] = parse(Int, num1[j])\n",
    "    end    \n",
    "    ising_steps[k1+1,:]=ising[:]\n",
    "    e_steps[k1 + 1], m_steps[k1 + 1] = calculate(ising, nbor1, nbor2, nbor3, J1, J2, J3, N)\n",
    "end\n",
    "\n",
    "min_energy, index = findmin(e_steps)\n",
    "ising_steps[index,:]\n",
    "configuration = ising_steps[index, :]\n",
    "\n",
    "print(configuration)\n",
    "println(\"\\n\")\n",
    "count_min_energy = count(x -> x == min_energy, e_steps)\n",
    "println(\"The minimum energy appears $count_min_energy times.\\n\")\n",
    "\n",
    "# Step 3: Retrieve configurations corresponding to the minimum energy\n",
    "indices = findall(x -> x == min_energy, e_steps)\n",
    "min_configurations = ising_steps[indices, :]\n",
    "\n",
    "println(\"Configurations corresponding to the minimum energy values:\")\n",
    "println(\"\\n\")\n",
    "for i in  1:count_min_energy\n",
    "println(min_configurations[i,:])\n",
    "end \n",
    "\n",
    "\n",
    "#filename = joinpath(save_dir, \"config_J2_$(round(J2, digits=2))_J3_$(round(J3, digits=2)).txt\")\n",
    "#open(filename, \"w\") do file\n",
    "#    writedlm(file, configuration', ' ') \n",
    "#end\n",
    "#m = sum(configuration)\n",
    "\n",
    "#push!(results, [J2 / J1, J3 / J1, m])\n",
    "\n",
    "#push!(final_results, results[end])\n",
    "\n",
    "#println(results)\n",
    "#end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "9f3da188-d4d1-4e57-893e-1069022eff76",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0, 0.8660254037844386, 1.7320508075688772, 2.598076211353316, 0.0, 0.8660254037844386, 1.7320508075688772, 2.598076211353316, 0.0, 0.8660254037844386, 1.7320508075688772, 2.598076211353316, 0.0, 0.8660254037844386, 1.7320508075688772, 2.598076211353316]\n",
      "\n",
      "\n",
      "[0.0, -0.5, 0.0, -0.5, 1.0, 1.5, 1.0, 1.5, 3.0, 2.5, 3.0, 2.5, 4.0, 4.5, 4.0, 4.5]\n"
     ]
    }
   ],
   "source": [
    "using DelimitedFiles\n",
    "\n",
    "function generate_coordinates(N, M)\n",
    "    x_coords = zeros(N, M)\n",
    "    y_coords = zeros(N, M)\n",
    "    \n",
    "    for i in 1:N\n",
    "        if i % 2 == 1  # Odd rows\n",
    "            base_value = (i - 1) * 1.5\n",
    "        else  # Even rows\n",
    "            base_value = (i - 2) * 1.5 + 1\n",
    "        end\n",
    "        \n",
    "        for j in 1:M\n",
    "            x_coords[i, j] = (j - 1) * sqrt(3) / 2\n",
    "            \n",
    "            if i % 2 == 1  \n",
    "                y_coords[i, j] = j % 2 == 1 ? base_value : base_value - 0.5\n",
    "            else  \n",
    "                y_coords[i, j] = j % 2 == 1 ? base_value : base_value + 0.5\n",
    "            end\n",
    "        end\n",
    "    end\n",
    "    \n",
    "    return x_coords, y_coords\n",
    "end\n",
    "\n",
    "N = 4 \n",
    "M = 4\n",
    "\n",
    "x_coords, y_coords = generate_coordinates(N, M)\n",
    "# print(x_coords)\n",
    "x = reshape(x_coords', :)\n",
    "\n",
    "# println(\"X Coordinates:\")\n",
    "# println(x_coords)\n",
    "# println(\"Y Coordinates:\")\n",
    "y = reshape(y_coords', :)\n",
    "# println(y_coords)\n",
    "println(x)\n",
    "println(\"\\n\")\n",
    "println(y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "98be1b23-590a-43ad-a118-41a075103c03",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using Plots\n",
    "\n",
    "# 给定的坐标信息\n",
    "x = [0.0, 0.8660254037844386, 1.7320508075688772, 2.598076211353316, 0.0, 0.8660254037844386, 1.7320508075688772, 2.598076211353316, 0.0, 0.8660254037844386, 1.7320508075688772, 2.598076211353316, 0.0, 0.8660254037844386, 1.7320508075688772, 2.598076211353316]\n",
    "y = [0.0, -0.5, 0.0, -0.5, 1.0, 1.5, 1.0, 1.5, 3.0, 2.5, 3.0, 2.5, 4.0, 4.5, 4.0, 4.5]\n",
    "\n",
    "# 自旋配置数据\n",
    "spin_configurations = [\n",
    "    [0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0],\n",
    "    [1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 1.0],\n",
    "    [1.0, 2.0, 1.0, 2.0, 2.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0, 2.0, 1.0, 2.0, 1.0],\n",
    "    [2.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0, 2.0, 1.0, 2.0, 1.0, 1.0, 2.0, 1.0, 2.0]\n",
    "]\n",
    "\n",
    "# 颜色映射：0 映射为蓝色，1 映射为红色，2 映射为绿色\n",
    "color_mapping = Dict(0.0 => :blue, 1.0 => :red, 2.0 => :green)\n",
    "\n",
    "# 循环绘制每个自旋配置的散点图\n",
    "for i in 1:length(spin_configurations)\n",
    "    p = plot()\n",
    "    z = spin_configurations[i]\n",
    "    colors = [color_mapping[z_i] for z_i in z]\n",
    "    scatter!(x, y, color = colors, aspect_ratio = 1)\n",
    "    display(p)\n",
    "end    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b9c7e41-d562-4273-bb03-9bd56110c3ce",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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